I guess that polygon's layer are going to define your atlas, so I made an example based on that.
Join attributes of the atlas layer with those objects (points and lines) that are inside. It should be something like this (I just did an example with points):

Go to properties/simbology and select rule-based and edit it like this image. It means that just those points that belongs to their atlas page are going to be shown.

Las step is to generate the atlas selecting the joined attribute as page name.

There are other ways but I think that this here is preaty easy to do it. Do the same with lines or other layers.